If that's at home, your neighbor has wifi on the same channel. All radio frequency stuff is based on signal-to-noise ratio and transmission pulses, and both of those must work correctly to get reception. If you have a decent signal, but the transmission pulses are being drowned out by a neighbor on the same channel, you'll get long delays and dropouts.
So first thing to do would be try changing the channel on your wifi transmitter. It should be in advanced settings somewhere. If it's set to "Auto", the auto setting looks for a channel with the best signal-to-noise ratio, rather than which channel is least busy (to do that, the router would have to stop and "listen" for 2-3 minutes at each startup, which isn't ideal). You could have a neighbor with a very weak signal transmitting on the same channel, but they're close enough that the interruption is constant, so both signals get interrupted.
Update: Nothing was really wrong with the WiFi. I took it to the SC and they downloaded the updated. It was the first update since I bought the car, a month ago. The car, with the same wifi has had 2 updates since then that went through with no issues.
As for mine, I decided to try an experiment and, after unplugging, I powered off the car and left it (don’t know if it stayed powered off since I used the app to lock it). A few hours later, I got a software update notification!
It was in my garage and, as far as I know, was using the WiFi.
If the progress bar ever stalls again, I’ll have to see if powering down is a repeatable solution but I hope it was just an oversized update.